Exponential Decay
General Properties of Exponential Decay Equation:
y = a(bx)
a = initial amount or population
b = decay factor (0 < b < 1)
y = future amount or population
x = number of times 'a' has decreased
To calculate x, use the equation
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑥 = 𝑡𝑖𝑚𝑒 𝑖𝑡 𝑡𝑎𝑘𝑒𝑠 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑔𝑟𝑜𝑤𝑡ℎ 𝑝𝑒𝑟𝑖𝑜𝑑
DO IT NOW!
Nuclear power plants use Uranium-239 as a power source.
U-239 has a half-life of about 2 years.
a) Complete the chart for the amount of 1000mg sample that will be left after 10 years.
Years, x
# of half-life periods
0
2
4
6
8
10
0
1
2
b) Graph the relation.
Mass (mg) of U-239
remaining, y
1000
500
c) Write an equation to model this growth
d) How much remains after 25 years?
Ex1: Plutonium-239 has a half-life of 24 years. Find the amount of a 50mg sample left after 35 years.
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If exponential decay is given as a percent use the equation:
y = a(1 - r)x
a = initial amount
r = growth rate (given as a percent)
x = # of times "a" has been decreased
Ex 2: You buy a new car for $24,000. The value of the car decreases by 16% every year.
How much will the car be worth in 8 years?
Ex 3: An adult takes 400mg of Advil. Each hour, the amount of Advil in the adult's system
decreases by about 29%. How much Advil will be left after 4 hours?
Ex 4: U-239 has a half-life of about 2 years. If you start with a 1000 mg sample, how long will
it take to decay to 10 mg?